## Chapter 4 - Counting Methods

**Prescribed Learning Outcomes:**

C4 – Solve problems that involve the fundamental counting principle.

C5 – Solve problems that involve permutations.

C6 – Solve problems that involve combinations.

## 4.1 - Counting Principles

The counting principle is used when you have several options available within one choice. For example, to get dressed in the morning you choose pants, a shirt, shoes, and a jacket. However, you have more than one possibility for each of the choices you have to make. That is when the counting principle is useful.

Please watch the counting principle video now.

Please do 4.1 page 235 #4-16.

Please watch the counting principle video now.

Please do 4.1 page 235 #4-16.

## 4.2 - Introducing Permutations and Factorial Notation

This section only introduces the concept of permutations but it very thoroughly discusses using factorial notation.

Please watch the permutations and factorial video now.

Please do 4.2 page 244 #5-14.

Please watch the permutations and factorial video now.

Please do 4.2 page 244 #5-14.

## 4.3 - Permutations When All Objects Are Distinguishable

Distinguishable objects means that they are all different.

Please watch the permutations involving different objects video.

Please do 4.3 page 255 #5-16.

Please watch the permutations involving different objects video.

Please do 4.3 page 255 #5-16.

## 4.4 - Permutations When Objects Are Identical

When a group of objects has some items that are identical, they can be switched without there being any noticeable difference in the arrangement. For this reason, we need to treat these groups differently than groups with all different objects.

Please watch the permutations of identical objects video.

Please do 4.4 page 267 #4-12.

Please watch the permutations of identical objects video.

Please do 4.4 page 267 #4-12.

## 4.5 - Exploring Combinations

An ice cream cone with chocolate on the bottom and vanilla on the top is a different

Combination - a grouping of objects where

There will be more permutations than combinations for a group of items.

Example 1: The letters ABC yield the following 3-letter permutations: ABC, ACB, BAC, BCA, CBA, CAB. However, those are all considered one combination.

Example 2: The letters ABC yield the following 2-letter permutations: AB, BA, AC, CA, BC, CB. However, there are only the following 2-letter combinations: AB, AC, BC.

Please do 4.5 page 272 #1-4.

**than an ice cream come with vanilla on the bottom and chocolate on the top. However, both are considered the same***permutation**of ice cream.***combination**Combination - a grouping of objects where

__order does not matter__.There will be more permutations than combinations for a group of items.

Example 1: The letters ABC yield the following 3-letter permutations: ABC, ACB, BAC, BCA, CBA, CAB. However, those are all considered one combination.

Example 2: The letters ABC yield the following 2-letter permutations: AB, BA, AC, CA, BC, CB. However, there are only the following 2-letter combinations: AB, AC, BC.

Please do 4.5 page 272 #1-4.

## 4.6 - Combinations

Reminder: when the order of a group of objects does not matter, then you should use combinations to find out how many different groupings you can have.

Please watch the combinations video.

Please do 4.6 page 280 #4-18.

Please watch the combinations video.

Please do 4.6 page 280 #4-18.

## 4.7 - Solving Counting Problems

Solving counting problems involves a variety of methods: factorial, combinations, and reasoning (using cases).

Remember to when considering more than one case, you add the results of each case.

However, when considering the different parts of one case, you multiply.

Please watch the solving counting problems video

Please do 4.7 page 288 #4-16.

Remember to when considering more than one case, you add the results of each case.

However, when considering the different parts of one case, you multiply.

Please watch the solving counting problems video

Please do 4.7 page 288 #4-16.